String Assignment is to the right hand what Position is to the left hand.  The three playing fingers (i, m, and a) are each assigned a string.  Whenever that particular string is to be played, it is the assigned finger's duty.  This allows the right hand to remain still in space.  There are four different string assignments. 

Listed in order of frequency of occurrence, they are:

Standard String Assignment (SSA) - i,m, and a on the 3rd, 2nd, and 1st strings, respectively

Upper String Assignment (USA) - i and m on the 2nd and 1st strings, respectively. 
Note that in this second most common String Assignment the "a" finger is not used.

Inner String Assignment (ISA) - i,m, and a on the 4th, 3rd, and 2nd strings, respectively

Lower String Assignment (LSA) - i,m, and a on the 5th, 4th, and 3rd strings, respectively

String Assignment is usually used when the right hand is playing arpeggios.  When the right hand is playing melodies, Rest Stroke Alternation is usually used.  It is a rare occasion when neither of these techniques are employed so it is a good idea to think of them as being binary - if you are not Alternating, you are in some form of String Assignment and vice versa.